Question

Investment X offers to pay you $5,100 per year for nine years, whereas Investment Y offers to pay you $7,200 per year for five years.

 

Calculate the present value for Investments X and Y if the discount rate is 6 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

Present value Investment X $ Investment Y $ 

Calculate the present value for Investments X and Y if the discount rate is 16 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

Present value Investment X $ Investment Y $

Answer 1

PV of annuity formula

PV = Annuity*(1-1/(1+r)^n)/r

Investment X

PV = 5100*(1-1/1.06^9)/0.06 =34688.63

Investment Y

PV =7200*(1-1/1.06^5)/0.06=30329.02

At 16% rate

Investment X

PV = 5100*(1-1/1.16^9)/0.16 =23493.37

Investment Y

PV =7200*(1-1/1.16^5)/0.16=23574.91

Answer 2

PV of an annuity is mathematically represented as:

PV =

[1-(4+5)-) [1-(1+r)-n LT P= Periodic Payment r=rate per period n = number of periods

a) r = 6%

Investment X

PV = 5100* (1 + 0.06) -9 0.06

PV = 5100 * 6.8017

PV = $34,688.63

Investment Y

PV = 7200* (1 + 0.06) -5 0.06

PV = 7200 * 4.2124

PV = $30,329.02

a) r = 16%

Investment X

PV = 5100 * 1-(1 + 0.16) -9 PV = 5100* 0,16

PV = 5100 * 4.6065

PV = $23,493.37

Investment Y

PV = 7200 * 1-(1 + 0.16)-5 PV = 7200* 0,16

PV = 7200 * 3.2743

PV = $23,574.91